In how many ways can the letter of the word SECTION be arranged if the consonants must always be in the order in which they occur in the word itself?

Answer 1

without restrictions there would be 7! ways or 5040

The EIO can be arranged in 3! or 6 ways, but we want only one of these sequences.

so the number of arrangements is 5040/6 = 840

(somebody check my thinking on this)

Answer 2

thank you

Answer 3

wrong its 210

Answer 4

Don't know why, that's just what the back of the book says :s

Answer 5

S E C T I O N
Total number of letters = 7!
# of consonants is 4! (S,c,t,n)
7!/4!= 210